Metabolic physiology asserts that body weight stability is achieved when over time the average absorbed energy intake equals the average expended energy. This principle, known as energy balance, justifies the design of numerous investigations that aim to elucidate the biology of obesity. The present work provides a mathematical analysis that demonstrates, nonetheless, that weight stability must coexist with a constant energy imbalance, i.e., the average absorbed energy intake and the average expended energy are significantly different during steady weight periods. This analytical finding is not in contradiction with the First Law of Thermodynamics since open systems can manifest a stable mass in the absence of energy equilibrium. The effect of caloric imbalance on weight fluctuations is thus the result of its underlying net mass flux. The energy balance theory is, consequently, an inconsistent paradigm; and as such, the data analysis and interpretation that follows from its postulates is expected to be erroneous.

The Wright-Fisher binomial model of allele frequency change is often approximated by a scaling limit in which selection, mutation and drift all decrease at the same 1/N rate. This construction restricts the applicability of the resulting 'Wright-Fisher diffusion equation' to the weak selection, weak mutation regime of evolution. We argue that diffusion approximations of the Wright-Fisher model can be used more generally, for instance in cases where genetic drift is much weaker than selection. One important example of this regime is Muller's ratchet phenomenon, whereby deleterious mutations slowly but irreversibly accumulate through rare stochastic fluctuations. Using a modified diffusion equation we derive improved analytical estimates for the mean click time of the ratchet.

Due to its implication in cancer treatment, the Warburg Effect has received extensive in silico investigation. Flux Balance Analysis (FBA), based on constrained optimization, was successfully applied in the Warburg Effect modelling. Yet, the assumption that cell types have one invariant cellular objective severely limits the applicability of the previous FBA models. Meanwhile, we note that cell types with different objectives show different extents of the Warburg Effect. To extend the applicability of the previous model and model the disparate cellular pathway preferences in different cell types, we built a Nonlinear Multi-Objective FBA (NLMOFBA) model by including three key objective terms (ATP production rate, lactate generation rate and ATP yield) into one objective function through linear scalarization. By constructing a cellular objective map and iteratively varying the objective weights, we showed disparate cellular pathway preferences manifested by different cell types driven by their unique cellular objectives, and we gained insights about the causal relationship between cellular objectives and the Warburg Effect. In addition, we obtained other biologically consistent results by using our NLMOFBA model. For example, augmented with the constraint associated with inefficient mitochondria function, low oxygen availability, or limited substrate, NLMOFBA predicts cellular pathways supported by the biology literature. Collectively, our NLMOFBA model can help build a complete understanding towards the Warburg Effect in different cell types. Finally, we investigated the impact of glutaminolysis, an important pathway related to glycolysis, on the occurrence of the Warburg Effect by using linear programming.

The establishment of a recent theoretical model of a coupled cortical thalamic network is an important step in the spatiotemporal dynamics of the brain. However, choosing the coupling distances and parameters for deep brain stimulation remains a very challenging task. This study aimed to establish a coupled cortical thalamic model with uncertain coupling distances. Utilizing different pathways formed by the pyramidal neuronal population, thalamic reticular nucleus, and thalamic relay nucleus, we reduced epileptic seizures with spike-wave discharges (SWDs) at 2-4 Hz. In modelling terms, numerical simulations demonstrated that a combination (1/3, 1/9) of the left and right ventricles is the optimal coupling distance of the proposed model by analyzing the percentage of SWDs. In simulation terms, on the one hand, the number of SWDs is inversely proportional to the amplitude; on the other hand, the number of SWDs shows a U-shaped trend with the change in frequency. The present study provides an important theoretical basis and direction for the future treatment of absence epilepsy. In brief, our simulation results will hopefully provide some help to patients.

BACKGROUND: The cyclic nucleotides cAMP and cGMP inhibit platelet activation. Different platelet signaling modules work together. We develop here a modelling framework to integrate different signaling modules and apply it to platelets. RESULTS: We introduce a novel standardized bilinear coupling mechanism allowing sub model debugging and standardization of coupling with optimal data driven modelling by methods from optimization. Besides cAMP signaling our model considers specific cGMP effects including external stimuli by drugs. Moreover, the output of the cGMP module serves as input for a modular model of VASP phosphorylation and for the activity of cAMP and cGMP pathways in platelets. Experimental data driven modeling allows us to design models with quantitative output. We use the condensed information about involved regulation and system responses for modeling drug effects and obtaining optimal experimental settings. Stepwise further validation of our model is given by direct experimental data. CONCLUSIONS: We present a general framework for model integration using modules and their stimulus responses. We demonstrate it by a multi-modular model for platelet signaling focusing on cGMP and VASP phosphorylation. Moreover, this allows to estimate drug action on any of the inhibitory cyclic nucleotide pathways (cGMP, cAMP) and is supported by experimental data.

Parental care is essential for biological systems. Marital bliss is one of the ideal paradigms for parental care, in which males contribute in raising offspring and females require a courtship time. Yet marital bliss state is neither Nash equilibrium nor Pareto optimum for the classic Battle of the Sexes. It thus leads to a gap between evolutionary theory and marital bliss. Previous works concentrate on the pairwise interactions between the two sexes to fill this gap, such as the courtship time and encounter rate. The social relationships within the same sex, however, receives much less attention. Here we investigate how social relationships within the same sex change marital bliss by introducing the coevolution of strategy and social network. Based on the time scale separation, it is found that a symmetric game is emergent via social adjustments within each sex, and the evolutionary outcome is determined by the interplay between the emergent symmetric game and the Battle of the Sexes. We find that marital bliss can be promoted when males are rational (strong selection limit) and females are irrational (weak selection limit); the stable Coy-Coy social relationships both stabilize and speed up marital bliss; the general criterion of stabilizing marital bliss for arbitrary imitation function are found, which are verified by simulations. Furthermore, the emergent symmetric games are insightful for determining whether the stable marital bliss is global stable. Our work provides an alternative avenue to facilitate marital bliss, which can be applied for general asymmetric games on dynamical networks.

Theoretical models were developed to propose a new mechanism enhancing mixed mating (reproduction by both outcrossing and selfing) in hermaphroditic plants; mixed mating can be maintained if there exists among-parent variation in early-acting inbreeding depression in embryos and parents can replace dead embryos by overproduction of ovules. In the two main models developed, the number of embryos produced is allowed to evolve, parents may overproduce embryos, and among-parent variation in early-acting inbreeding depression does not exist or exists. I found that mixed mating does not evolve if among-parent variation in early-acting inbreeding depression does not exist, whereas it evolves if it exists. If the degree of early-acting inbreeding depression in embryos is variable among parents, parents with the same selfing strategy suffer different effects of early-acting inbreeding depression. Specifically, overproduction of embryos may be insufficient when inbreeding depression is severe but wasteful when it is weak. Hence, it is advantageous to produce a moderate number of embryos to reduce waste of resources. Mixed mating is then advantageous to avoid great reductions in seed number caused by massive loss of selfed embryos in cases of severe inbreeding depression.